Submission date: 23 April 2020

Abstract:

We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas without parameters in the theory of Real Closed Fields. The third result, unexpectedly, requires the Hironaka's theorem on resolution of singularities.

Mathematics Subject Classification: Primary: 03C64. Secondary: 03C45, 03C10

Keywords and phrases: real closed fields, ordered structures, stable formulas

Full text arXiv 2004.10953: pdf, ps.